Séminaire d'Homotopie et Géométrie Algébrique

The stable cohomology of block diffeomorphisms of connected sums of $S^k \times S^l$

by Robin Stoll (Stockholm University)

Europe/Paris
IMT 1R2 207 (Salle Pellos)

IMT 1R2 207

Salle Pellos

Description
I will explain an identification of the stable rational cohomology of the classifying spaces of self-equivalences as well as block diffeomorphisms of connected sums of S^k × S^l (relative to an embedded disk), where 2 < k < l < 2k–1. The result is expressed in terms of versions of Lie graph complex homology, the constructions of which I will recall.
 
This also leads to a computation, in a range of degrees, of the stable rational cohomology of the classifying spaces of diffeomorphisms of these manifolds. In the case l = k+1, this recovers and extends recent results of Ebert-Reinhold.
 
If time permits, I will explain parts of the proof; this includes in particular work joint with Berglund on a certain type of algebraic models for relative self-equivalences, inspired by results of Berglund-Zeman.